(-4a^2)(2a^-3)^-4

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (-4a^2)(2a^-3)^-4

This article will guide you through simplifying the mathematical expression (-4a^2)(2a^-3)^-4. We'll break down the process step by step using the rules of exponents.

Understanding the Properties of Exponents

Before we begin, let's review the key properties of exponents that will be used:

• Product of powers: x^m * x^n = x^(m+n)
• Power of a power: (x^m)^n = x^(m*n)
• Negative exponent: x^-n = 1/x^n

Simplifying the Expression

1. Simplify the inner exponent:

   (-4a^2)(2a^-3)^-4 = (-4a^2)(2^-4 * a^(-3*-4))

   Applying the power of a power rule, we get:

   (-4a^2)(2^-4 * a^12)

2. Simplify the negative exponent:

   (-4a^2)(1/2^4 * a^12)

   Using the negative exponent rule, we obtain:

   (-4a^2)(1/16 * a^12)

3. Multiply the coefficients and combine the variables:

   (-4/16) * (a^2 * a^12)

   Using the product of powers rule, we simplify:

   (-1/4) * a^(2+12)

4. Final simplification:

   (-1/4) * a^14 = -1/4 * a^14

Conclusion

Therefore, the simplified expression of (-4a^2)(2a^-3)^-4 is -1/4 * a^14. By applying the properties of exponents, we can effectively simplify complex expressions and express them in a more concise form.